The judgment of conscience
57. "The text of the Letter to the Romans which has helped us to grasp the essence of the natural law also indicates the biblical understanding of conscience, especially in its specific connection with the law: "When Gentiles who have not the law do by nature what the law requires, they are a law unto themselves, even though they do not have the law. They show that what the law requires is written on their hearts, while their conscience also bears witness and their conflicting thoughts accuse or perhaps excuse them" (Rom 2:14-15)."
"According to Saint Paul, conscience in a certain sense confronts man with the law, and thus becomes a "witness" for man: a witness of his own faithfulness or unfaithfulness with regard to the law, of his essential moral rectitude or iniquity. Conscience is the only witness, since what takes place in the heart of the person is hidden from the eyes of everyone outside. Conscience makes its witness known only to the person himself. And, in turn, only the person himself knows what his own response is to the voice of conscience."
When unbelievers today -- atheists, agnostics, those who do not believe in one eternal all-powerful God who created heaven and earth, as well as the non-practicing nominal members of various religions -- when these unbelievers make a decision to do good, or to do evil, they are not excused from the requirement to obey the eternal moral law. Even if they do not know the teachings of any true religion on morality, they have the ability to use reason and free will to discern right from wrong.
Their conscience might accuse them, if they knowingly choose what they understand to be immoral, or if they refuse to even consider that their acts may be immoral. Their conscience might excuse them, if they committed an objectively immoral act without realizing that it was immoral. But they are not exempt from the eternal moral law.
Roman Catholic theologian